Active Multi-Information Source Bayesian Quadrature
Active Multi-Information Source Bayesian Quadrature
复制标题
主动多信息源贝叶斯求积
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Maren Mahsereci
中科院分区：
文献类型：
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作者：
A. Gessner;Javier I. González;Maren Mahsereci
贝叶斯求积(BQ)是一种样本有效的概率数值方法，用于求解代价昂贵的黑盒函数的积分，但到目前为止，主动BQ学习方案只关注被积函数本身作为信息源，不允许从较便宜的相关函数传递信息。在这里，我们在BQ中设置了当可访问多个相关的可变成本信息源(在输入和源中)时的主动学习场景。例如，当评估被积函数需要运行复杂的模拟时，就会出现这种设置，这种模拟可以通过以较低的复杂程度和较低的成本进行模拟来近似。我们构造了有意义的成本敏感的多源采集率，作为对普通效用函数的扩展，并讨论了盲目推广所产生的陷阱。此外，我们还证明了VBQ获取策略是所有考虑的代价敏感的获取策略的一个角落情况，在单一来源和不变成本的情况下，这些策略崩溃为一个单一的退化策略。在概念验证实验中，我们仔细检查我们的广义获取函数的行为。在一个流行病学模型上，我们证明了主动多源BQ(AMS-BQ)比VBQ更有效地分配预算，以学习积分以获得更好的精度。
Bayesian quadrature (BQ) is a sample-efficient probabilistic numerical method to solve integrals of expensive-to-evaluate black-box functions, yet so far,active BQ learning schemes focus merely on the integrand itself as information source, and do not allow for information transfer from cheaper, related functions. Here, we set the scene for active learning in BQ when multiple related information sources of variable cost (in input and source) are accessible. This setting arises for example when evaluating the integrand requires a complex simulation to be run that can be approximated by simulating at lower levels of sophistication and at lesser expense. We construct meaningful cost-sensitive multi-source acquisition rates as an extension to common utility functions from vanilla BQ (VBQ),and discuss pitfalls that arise from blindly generalizing. Furthermore, we show that the VBQ acquisition policy is a corner-case of all considered cost-sensitive acquisition schemes, which collapse onto one single de-generate policy in the case of one source and constant cost. In proof-of-concept experiments we scrutinize the behavior of our generalized acquisition functions. On an epidemiological model, we demonstrate that active multi-source BQ (AMS-BQ) allocates budget more efficiently than VBQ for learning the integral to a good accuracy.
概率数值学和计算中的不确定性。
DOI：
10.1098/rspa.2015.0142
发表时间：
2015-07-08
期刊：
Proceedings. Mathematical, physical, and engineering sciences
影响因子：
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作者：
Hennig P;Osborne MA;Girolami M
通讯作者：
Girolami M